Real Quantum Theory Alone Permits Genuinely New Causal Connections

A reversal of the established hierarchy between real and complex quantum theories has been demonstrated when considering indefinite causal order. Jacopo Surace and colleagues at Aix-Marseille University show that real quantum theory can generate strictly more process correlations than complex quantum theory, challenging conventional understanding of quantum information processing. The research, utilising the process-matrix framework and exploring the impact of symmetry constraints on local quantum operations, reveals a key dichotomy between finite unitary symmetries and real quantum theory. It demonstrates genuinely new correlations arising from indefinite causality.

Real quantum theory surpasses complex theory via indefinite causal order

The Lazy Guess Your Neighbour’s Input (LGYNI) causal inequality was exceeded, clearly separating real and complex quantum theories. Previously, complex quantum theory outperformed real quantum theory regarding process correlations under fixed causal order. This hierarchy is now reversed, demonstrating real quantum theory can generate more correlations with indefinite causal order. An explicit finite-dimensional process strategy witnesses this finding, proving real quantum theory achieves outcomes impossible for complex quantum theory under identical conditions.

A dichotomy now exists, as finite unitary symmetries do not generate genuinely new correlations, but real quantum theory does, highlighting the unique capabilities arising from indefinite causality. Specifically, a finite-dimensional process strategy within real quantum theory achieves outcomes impossible for comparable complex quantum strategies, evidenced by exceeding the dimension-independent upper bound for the LGYNI causal inequality. This builds upon previous investigations into symmetry constraints, such as those arising from missing reference frames or superselection rules, which limit operations available in local laboratories. These studies explored how these restrictions impact valid quantum processes, finding symmetries enlarge the admissible process cone, the range of possible quantum behaviours. Current results focus on simplified scenarios and do not yet demonstrate a pathway towards building practical quantum devices utilising this advantage. The process-matrix framework underpinned this, defining valid processes by what local laboratories can implement without assuming a fixed causal order, expressed mathematically as Cproc,fin QT ⊊Cproc,fin RQT, indicating real quantum theory can achieve outcomes impossible within standard complex quantum theory under these conditions.

Real quantum theory surpasses complex quantum theory with indefinite causal structure

Real quantum theory generates more process correlations than complex quantum theory when causal order is indefinite, reversing a previously established hierarchy. The authors clarify this reversal applies specifically to indefinite causal order, contrasting with prior research showing complex quantum theory to be strictly richer with a fixed causal order. Restricting local operations via symmetry constraints simultaneously weakens validity constraints and limits probing capabilities, leading to this distinction.

The research acknowledges a focus solely on the implications of real quantum theory, without exploring whether other symmetry constraints might also lead to similar reversals. Furthermore, the authors detail that while they prove a mathematical relationship demonstrating enhanced correlations, they do not currently address potential practical applications or experimental verification of these findings. This establishes that real quantum theory, a simplified model excluding imaginary numbers, can generate stronger correlations than standard complex quantum theory when the order of cause and effect is not fixed. By employing the process-matrix framework, which defines quantum processes by what is physically achievable than pre-defined sequences, a reversal of a long-held hierarchy was demonstrated. This finding proves that symmetries restricting local quantum operations do not enhance correlations, but real quantum theory uniquely does, exceeding established bounds like the Lazy Guess Your Neighbour’s Input inequality.

Real quantum supremacy via indefinite causal order and symmetry constraints

Real quantum theory can achieve outcomes impossible within standard complex quantum theory when the order of cause and effect is not fixed. This reverses a previously established hierarchy where complex quantum theory was considered strictly richer than its real counterpart under fixed causal order. The research utilizes the process-matrix framework, a method for formalising quantum causality without assuming a predetermined order of events. Cproc,fin QT ⊊Cproc,fin RQT signifies that real quantum theory generates finite-dimensional process correlations that complex quantum theory cannot reproduce.

Future research, as suggested by the authors, will explore the implications of these findings for quantum causality and foundational quantum theory, explicitly positioning indefinite causal order as a distinctive element in the comparison between real and complex quantum theories. This establishes that real quantum theory, a simplified model excluding imaginary numbers, can generate stronger correlations than standard complex quantum theory when the order of cause and effect is not fixed. By employing the process-matrix framework, which defines quantum processes by what is physically achievable than pre-defined sequences, a reversal of a long-held hierarchy was demonstrated.

Real quantum theory, a model excluding imaginary numbers, was shown to generate stronger correlations than standard complex quantum theory when the order of cause and effect is indefinite. This reverses a previously understood hierarchy, demonstrating that real quantum theory can achieve outcomes impossible within the complex model. Researchers used the process-matrix framework to define quantum processes by physical achievability, rather than pre-defined sequences, to reach this conclusion. The authors intend to further investigate these findings in the context of quantum causality and foundational quantum theory.